Approximate Distance Oracles for Planar Graphs with Improved Query Time-Space Tradeoff

TL;DR

This paper introduces a new approximate distance oracle for planar graphs that significantly improves the query time-space tradeoff, achieving faster queries with less space compared to previous methods.

Contribution

It presents a (1+epsilon)-approximate distance oracle with improved query time and space complexity for planar graphs, surpassing prior results by reducing the product of query time and space.

Findings

Achieves O(n(loglog n)^2) space for the oracle.

Provides O((loglog n)^3) query time.

Improves previous product of query time and space from O(n log n) to O(n(loglog n)^5).

Abstract

We consider approximate distance oracles for edge-weighted n-vertex undirected planar graphs. Given fixed epsilon > 0, we present a (1+epsilon)-approximate distance oracle with O(n(loglog n)^2) space and O((loglog n)^3) query time. This improves the previous best product of query time and space of the oracles of Thorup (FOCS 2001, J. ACM 2004) and Klein (SODA 2002) from O(n log n) to O(n(loglog n)^5).